The incident took place at around 5 AM. Flight 9W 2374 which had arrived from Dubai and was bound for Mumbai, was about to take off when it skidded off the runway.
When the evacuation was on, the aircraft tilted forward, an eyewitness said, triggering panic among passengers.
Navy sources said 15 people suffered "minor injuries and fractures" in the process.
"Few guests have sustained minor injuries during the evacuation process and medical assistance is being coordinated by the Jet Airways team and the airport authorities," the airlines said in a statement.
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The airport has been closed for operations till 12.30 pm for all flight operations, airport sources said.
To put it in perspective, Airbus, the world's largest
aircraft-maker, has made only 10,000 planes so far.
The aircraft on the world tour has two Pratt & Whitney piston engines, Agullo said, adding that it has flown 74,500 hours. Engines of this make have to be changed after every 1200 hours, he said.
The DC-3 was also the first plane to complete the US east-west journey with just one stop. Out of the 16,000 DC-3 built, 10,000 were in the US, 487 in Japan and the rest in Russia.
Bezeley said the plane chose Nagpur for a halt because the city is at the heart of India, and also because the 'aviation gas', its fuel, is not available at large airports.
On Wednesday the plane will fly off to Chittagong in Bangladesh, from where it will head to Bangkok, Singapore, Hong Kong, China and Japan.
It will be stationed in Japan for a month before heading for the west coast of the US. In Tokyo, the plane will offer a joy ride to the child victims of the 2013 tsunami.